PIRSA:26090037 Scientific Series Quantum Gravity

DOI10.48660/26090037

Series: Quantum Gravity

Mrini, L. (2026). Canonical Quantization of Singular Configuration Spaces: Symmetry Reduction, Mass Gap Bounds, and Non-smooth Calculus. Perimeter Institute. https://pirsa.org/26090037

Mrini, Luca. Canonical Quantization of Singular Configuration Spaces: Symmetry Reduction, Mass Gap Bounds, and Non-smooth Calculus. Perimeter Institute, Sep. 10, 2026, https://pirsa.org/26090037 

@misc{ pirsa_PIRSA:26090037,
  doi = {10.48660/26090037},
  url = {https://pirsa.org/26090037},
  author = {Mrini, Luca},
  keywords = {Quantum Gravity},
  language = {en},
  title = {Canonical Quantization of Singular Configuration Spaces:  Symmetry Reduction, Mass Gap Bounds, and Non-smooth Calculus},
  publisher = {Perimeter Institute},
  year = {2026},
  month = {sep},
  note = {PIRSA:26090037 see, \url{https://pirsa.org}}
}

Abstract

In this work-in-progress, we study the quantization of singular configuration spaces, generalizing the canonical structures of smooth quantum mechanics. We develop a framework for constructing a Hilbert space of quantum states, generalized position and momentum operators, a kinetic-plus-potential Hamiltonian, unitary quantum dynamics, and a C*-algebra of observables under suitable assumptions. Our approach is based on the non-smooth calculus of metric-measure spaces formalized in recent years. One of our central contributions is a new technique to bound the mass gap of certain singular systems obtained via symplectic reduction by analyzing the curvature of the non-reduced configuration space. We illustrate our method for the harmonic oscillator constrained to zero angular momentum, lattice Yang--Mills theory, and fractional-dimensional Laakso spaces. To conclude, we speculate about future directions pertaining to the Yang--Mills mass gap problem and quantum gravity.
 

Resources

1/48
1/48
2/48
2/48
3/48
3/48
4/48
4/48
5/48
5/48
6/48
6/48
7/48
7/48
8/48
8/48
9/48
9/48
10/48
10/48
11/48
11/48
12/48
12/48
13/48
13/48
14/48
14/48
15/48
15/48
16/48
16/48
17/48
17/48
18/48
18/48
19/48
19/48
20/48
20/48
21/48
21/48
22/48
22/48
23/48
23/48
24/48
24/48
25/48
25/48
26/48
26/48
27/48
27/48
28/48
28/48
29/48
29/48
30/48
30/48
31/48
31/48
32/48
32/48
33/48
33/48
34/48
34/48
35/48
35/48
36/48
36/48
37/48
37/48
38/48
38/48
39/48
39/48
40/48
40/48
41/48
41/48
42/48
42/48
43/48
43/48
44/48
44/48
45/48
45/48
46/48
46/48
47/48
47/48
48/48
48/48

Next talk

Related Talks